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For the curious, I believe this works by doing a Fourier decomposition of both images. Then the composite image is produced by taking the low-frequency compone

by jnhnum1 15y ago

For the curious, I believe this works by doing a Fourier decomposition of both images. Then the composite image is produced by taking the low-frequency components from Monroe, and high-frequency components from Einstein. This way the "details" of the image look like Einstein, but the "overall" image looks more like Monroe.

jwn 15y ago
Not to take this off-topic, but I never understood how an image can be converted into a Fourier series. It always made sense for waves, but images?
- szany 15y ago
  Think of a black and white image like a surface. image :: (R, R) -> R
- dcosson 15y ago
  Imagine the waveform of a sound wave - there is an amplitude for each point in time, which you can easily take a FT of. This waveform could also be, say, a vibrating guitar string at a fixed moment in time, in which case the units are amplitude vs. distance, but it is still just a function that you can take a FT transform of (now the "frequency" domain is the inverse of distance rather than the inverse of time, but it still works). An image is just a function of amplitude vs. distance, though there are 2 distance variables since an image is 2-dimensional, but the idea is the same, and the Fourier Transform is still defined for functions of 2 or more variables. In a color jpeg, I believe this is done individually for red, blue, and green, and the point at which you cut off the infinite series of Fourier coefficients determines image quality. That said, this picture is awesome! I've never seen it done before.
- deleted 15y ago
  [deleted]
- augustl 15y ago
  Here's a thorough explanation, with illustrations. http://www.hackerfactor.com/blog/index.php?/archives/440-The-Perfect-Blend.html http://www.hackerfactor.com/blog/index.php?/archives/440-The...
- ZoFreX 15y ago
  I learnt fourier transforms as something done to 2D images before I learnt any other applications, so I can draw the FT of a simple image by hand, but I really struggle getting my head around other applications :(
- sghael 15y ago
  Images are just signals as a function of 2D space. So you can use the 2d FFT: http://fourier.eng.hmc.edu/e101/lectures/Image_Processing/node6.html http://fourier.eng.hmc.edu/e101/lectures/Image_Processing/no... Another idea to grok: a checkerboard pattern image where every other pixel row and column are alternating full black and full white represents the "highest frequency" image possible at that sample rate (pixel density). This is the 2d equivalent of an alternating sinusoid +1,-1,+1,-1, etc

by jnhnum1 15y ago

jwn 15y ago

Not to take this off-topic, but I never understood how an image can be converted into a Fourier series. It always made sense for waves, but images?

szany 15y ago
Think of a black and white image like a surface. image :: (R, R) -> R
dcosson 15y ago
Imagine the waveform of a sound wave - there is an amplitude for each point in time, which you can easily take a FT of. This waveform could also be, say, a vibrating guitar string at a fixed moment in time, in which case the units are amplitude vs. distance, but it is still just a function that you can take a FT transform of (now the "frequency" domain is the inverse of distance rather than the inverse of time, but it still works). An image is just a function of amplitude vs. distance, though there are 2 distance variables since an image is 2-dimensional, but the idea is the same, and the Fourier Transform is still defined for functions of 2 or more variables. In a color jpeg, I believe this is done individually for red, blue, and green, and the point at which you cut off the infinite series of Fourier coefficients determines image quality. That said, this picture is awesome! I've never seen it done before.
deleted 15y ago
[deleted]
augustl 15y ago
Here's a thorough explanation, with illustrations. http://www.hackerfactor.com/blog/index.php?/archives/440-The-Perfect-Blend.html http://www.hackerfactor.com/blog/index.php?/archives/440-The...
ZoFreX 15y ago
I learnt fourier transforms as something done to 2D images before I learnt any other applications, so I can draw the FT of a simple image by hand, but I really struggle getting my head around other applications :(
sghael 15y ago
Images are just signals as a function of 2D space. So you can use the 2d FFT: http://fourier.eng.hmc.edu/e101/lectures/Image_Processing/node6.html http://fourier.eng.hmc.edu/e101/lectures/Image_Processing/no... Another idea to grok: a checkerboard pattern image where every other pixel row and column are alternating full black and full white represents the "highest frequency" image possible at that sample rate (pixel density). This is the 2d equivalent of an alternating sinusoid +1,-1,+1,-1, etc